mplayer with all the win32 codecs will play .mp4, .mov
VLC will too as I recall.
Totem, Xine.. all of them should play .mp4, .mov with the all codecs package.
I think that I have heard buntu users say that there is a community repository that you need to include that has those. Do a search on LQ, I've seen this talked about over the years.
You might want to search/ask in the buntu forum.